CN107045290A - Reaction-regeneration system optimal control method based on MQPSO DMPC - Google Patents

Reaction-regeneration system optimal control method based on MQPSO DMPC Download PDF

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CN107045290A
CN107045290A CN201710448089.1A CN201710448089A CN107045290A CN 107045290 A CN107045290 A CN 107045290A CN 201710448089 A CN201710448089 A CN 201710448089A CN 107045290 A CN107045290 A CN 107045290A
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吴凌
周伟
白竣仁
陈实
陈雪梅
易军
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Chongqing University of Science and Technology
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    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention discloses a kind of reaction-regeneration system optimal control method based on MQPSO DMPC, including：S1：The transfer function model of reaction-regeneration system is converted into step response model；S2：Set up DMPC models, including open-loop prediction module, steady-state target calculation module and dynamic matrix control module；S3：Using MQPSO algorithms, on the premise of not relaxed constraints condition, economic optimization and the multi-goal optimizing function of energy resource consumption are solved；S4：The solution tried to achieve according to MQPSO algorithms to S3 multi-goal optimizing function, try to achieve the output setting value of reaction-regeneration system, and and reality output deviation as single goal error function, finally the single goal error function is solved using QPSO algorithms, the optimal varied amount of performance variable is obtained.The reaction-regeneration system optimal control method based on MQPSO DMPC that the present invention is provided not only reduces RRS hardware burdens, moreover it is possible to obtain more excellent performance variable parameter, and on the basis of ensureing economic benefit and reducing energy consumption, control is further optimized to RRS.

Description

Reaction-regeneration system optimal control method based on MQPSO-DMPC
Technical field
The invention belongs to technical field of petrochemical industry, it is related to a kind of reaction-regeneration system optimization control based on MQPSO-DMPC Method processed.
Background technology
Petrochemical industry occupies very important status in Chinese national economy, carries and provides various energy for China The heavy burden in source.Conventional catalytic cracking unit is made up of three parts, steady comprising reaction-regeneration system, fractionating system and absorption Determine system.It is used as the core of catalytic cracking, reaction-regeneration system (Reaction regeneration system, RRS) By crude oil by processing, various clean or whites are generated.But it is higher to there is energy consumption in existing reaction-regeneration system, and not Stable the problem of.
The content of the invention
In view of the above problems, control is optimized it is an object of the invention to provide a kind of reaction-regeneration system based on MQPSO-DMPC Method processed, the problem of to there is energy consumption higher to solve existing RRS, and unstable.
The reaction-regeneration system optimal control method based on MQPSO-DMPC that the present invention is provided, including：
S1：The transfer function model of reaction-regeneration system is converted into step response model；
S2：DMPC models are set up, DMPC models include open-loop prediction module, steady-state target calculation module and dynamic matrix control Molding block；
S3：Using MQPSO algorithms, on the premise of not relaxed constraints condition, to economic optimization and many mesh of energy resource consumption Mark majorized function is solved；Wherein, constraints includes the hard constraint and soft-constraint of performance variable, the hard constraint of controlled variable And soft-constraint, the constraint of external object；
S4：Reacted according to the solution that MQPSO algorithms are tried to achieve to the multi-goal optimizing function of economic optimization and energy resource consumption The output setting value of regenerative system, and and reality output deviation as single goal error function, using QPSO algorithms to the list Target error function is solved, and obtains the optimal varied amount of performance variable.
Using the above-mentioned reaction-regeneration system optimal control method based on MQPSO-DMPC provided according to the present invention, pass through RRS economy and energy consumption multi-goal optimizing function is set, and RRS multi-objective optimization question solved using MQPSO, is being protected Demonstrate,prove on the basis of economic benefit and reduction energy consumption, further the process to RRS carries out stable state control, i.e., using QPSO to DMPC The dynamic matrix control stage solve carrying out stable state control to RRS process.
Brief description of the drawings
Fig. 1 is the flow chart of the reaction-regeneration system optimal control method based on MQPSO-DMPC according to the present invention；
Fig. 2 is the tracking effect figure exported according to the DMPC of the present invention to RRS；
Fig. 3 is the tracking effect inputted according to the DMPC of the present invention to RRS；
Fig. 4 is the tracking result figure to RRS output according to MQPSO-DMPC of the invention；
Fig. 5 is according to the tracking result figure of MQPSO-DMPC of the invention to RRS output.
Embodiment
In the following description, for purposes of illustration, in order to provide the comprehensive understanding to one or more embodiments, explain Many details are stated.It may be evident, however, that these embodiments can also be realized in the case of these no details. In other examples, for the ease of describing one or more embodiments, known structure and equipment are shown in block form an.
Explanation of nouns
MQPSO：Multi-objective Quantum-behaved Particle Swarm Optimization Algorithm, multi-target quantum particle swarm optimization algorithm.
DMPC：The Double-layerd Model Predictive Control, bilayer model PREDICTIVE CONTROL.
QPSO：Quantum-behaved Particle Swarm Optimization algorithm, quantum particle swarm Optimized algorithm.
Fig. 1 shows the flow of the reaction-regeneration system optimal control method based on MQPSO-DMPC according to the present invention.
As shown in figure 1, the reaction-regeneration system optimal control method based on MQPSO-DMPC that the present invention is provided, including such as Lower step：
S1：RRS transfer function model is converted into step response model.
The step response model of RRS after conversion is as follows：
In formula (1), Δ u is the variable quantity of performance variable, and k is the time, and N is model length,For the rank of RRS performance variables Jump response coefficient matrix,It is right for the step-response coefficients matrix of RRS disturbance variablesMeet
S2：DMPC models are set up, DMPC models include open-loop prediction module, steady-state target calculation module and dynamic matrix control Molding block.
The process of open-loop prediction module is set up, is comprised the following steps：
S211：As Δ u (k+i-1)=0, Δ v (k+i-1)=0 (1≤i≤P), ifFor to y (k+p | k) Predicted value, wherein, Δ ν be disturbance variable variable quantity, P for prediction time domain, then have：
S212：Consider feedback compensation, it is assumed that vss(k)=vss(k-1)+Δ v (k) is, it is known that since the k moment, reaction is again When the performance variable of raw system no longer changes, the open-loop prediction for obtaining reaction-regeneration system based on formula (2) is yol(k+i | k), when The open-loop prediction for obtaining reaction-regeneration system is solved when detecting Δ u (k-1)：
S213：Reality output based on formula (3) Yu RRS, obtains error：
S214：First order exponential smoothing processing is carried out to error, obtained
Wherein, vss(k) it is the recurrence model of step response；
S215：On the basis of the error after smoothing processing, the output to RRS carries out feedback compensation, and feedback compensation is not It is all constant, note to carry out all time pointsIt is worth to for the open loop dynamic prediction at k moment：
S216：Convolution (4), obtains opening steady state predictions：
The process of steady-state target calculation module is set up, is comprised the following steps：
S221：Extract the performance variable of all reaction-regeneration systems and the hard constraint condition of controlled variable and soft-constraint bar Part, and merge the variable quantity δ u being expressed as on steady state operation variabless(k) form：
Wherein,For the upper limit of performance variable,For the set of the ideal value of performance variable,For steady-state gain square Battle array,For the variable quantity of stable state controlled variable,For the set of the ideal value of controlled variable, k is iterations, and t is Time.
More specifically, stable state MV hard constraint is：
In MPC control process, there is the constraint of MV rate of changesWherein, M To control time domain, then increased stable state MV hard constraint is：
To δ us(k) limited, then increased stable state MV hard constraint is：
Stable state CV hard constraint is：
Stable state CV soft-constraint is：
In real process, always meetIn addition, to Δ yss(k) limited, then increased Stable state CV hard constraint be
CV new steady-state value is only decided by δ uss(k) size, and, steady state predictive model unrelated with MV dynamic changes path For：
Wherein,For steady state gain matrix；For open loop steady state predictions；
All conditions merge the variable quantity δ u being expressed as on steady state operation variabless(k) form：
S222：Set up economic optimization J1J is consumed with energy consumption2Biobjective scheduling function：
In formula (5), B is weight.
S223：Relaxed constraints condition, is solved using QUADRATIC PROGRAMMING METHOD FOR to formula (5), obtains the stable state under multiple target The variable quantity δ u of performance variabless(k)。
The process of dynamic matrix control module is set up, is comprised the following steps：
S231：It is P to take prediction time domain, and it is M to control time domain.In each moment k, it can obtain：
S232：When P is more than N, yol(k+j | k)=yol(k+N | k), j ＞ N, the predicted value includes the feedback of predicated error Correction and the influence of interference, are obtained：
Wherein, D is dynamic control matrix；
S233：In dynamic matrix, economic optimization and the multi-goal optimizing function of energy resource consumption are asked according to MQPSO algorithms Solution obtain reaction-regeneration system output setting value, and and reality output deviation be used as single goal error function, selection The single goal error function of minimum is as follows：
In order to allow prediction output close to reality output, RRS output setting value and reality is tried to achieve with the solution of formula (5) The error of border output is single goal error function.
S234：The object function (6) of minimum is solved, the optimal varied amount of steady state operation variable is obtained.
MATLAB7.0 is used for emulation platform, using RRS as object, carries out in the research of DMPC algorithms, simulation process, adopts The sample cycle is 4 minutes, weight vectors B=(122211), Jmin=-3, model time domain N=30, make variable lower limitui For 0, prediction The performance variable of controlThe upper limit is 600, controlled variable lower limityi For 0, the controlled variable upper limitFor 800, steady state operation change quantitative change Change value δ us(k) it is 100, performance variable changing value is 50.
It is as shown in table 1 that each performance variable represents title：
Each performance variable of table 1 represents title
It is as shown in table 2 that each controlled variable represents title：
Each controlled variable of table 2 represents title
By experiment simulation, tracking effects of the DMPC to output and the tracking effect to input are as shown in Figures 2 and 3.
From figures 2 and 3, it will be seen that under conditions of each variable priority orders are considered, passing through relaxed constraints condition pair Optimal performance variable variable quantity is asked for, and simulation result shows, inputs and output of the DMPC to RRS have tracking effect well Really.However, relaxed constraints condition not only proposes higher requirement to hardware device, and required optimal solution is by loosening The optimal solution asked for after constraints, is not optimal solution truly.Swarm Intelligence Algorithm is in not relaxed constraints condition Under, there is natural advantage than traditional quadratic programming or linear programming method to the solution of optimization problem, therefore, the present invention will MQPSO algorithms are incorporated into DMPC.
S3：Using MQPSO algorithms, on the premise of not relaxed constraints condition, to economic optimization and many mesh of energy resource consumption Mark majorized function is solved.
Wherein, hard constraint and soft-constraint of the constraints including performance variable, the hard constraint and soft-constraint of controlled variable, outside The constraint of portion's target.
S31：Systematic parameter, including population scale n, maximum iteration T are initialized, at random n particle x of generation1, x2..., xn, particle dimension m, compression-broadening factor α and make external archival collection Q, Q is sky；
S32：The fitness of each particle is evaluated, and individual optimal value and global optimum are replaced according to quality；
S33：By the current fitness p of each particleiWith individual adaptive optimal control degreeIt is compared, if current fitness piDominate individual adaptive optimal control degreeThen by current fitness piInstead of individual adaptive optimal control degreeOtherwise, original is retained Body adaptive optimal control degree
S34：External archival collection Q is updated, non-dominant collection all in population is added into external archival collection Q, and deletion is propped up The particle matched somebody with somebody；
S35：A particle is randomly choosed in external archival collection Q be used as global optimum by the use of press mechanism and Tabu search algorithm Value；
S36：Update the position x of the particle as global optimumij(t), more new formula is：
xij(t+1)=eij(t)±α|Cij(t)-xij(t)|×ln[1/uij(t)]
eij(t)=β Pij(t)+(1-β)Pgj(t)
Wherein, Cij(t) the average optimal position of all particles, x are representedij(t+1) it is denoted as the particle of global optimum Position after renewal, PijFor the current optimal location of i-th of particle jth dimension, PgjFor global optimum position, uijIt is respectively 0 with β Random number between to 1；α be expansion-contraction factor, the convergence of single particle can be influenceed, from 1 to 0.5 with iterations from Adapt to change；
S37：Judge whether current globally optimal solution meets condition or whether iterations reaches maximum iteration T, If it is, exporting current globally optimal solution, otherwise, jump to step S32 and computed repeatedly, until current globally optimal solution Meet condition or untill iterations reaches maximum iteration T；
S38：Relaxed constraints condition, does not utilize economic optimization Js of the MQPSO to foundation1J is consumed with energy consumption2Biobjective scheduling Function is solved, and tries to achieve the variable quantity δ u of the steady state operation variable under multiple targetss(k)。
S4：Reacted according to the solution that MQPSO algorithms are tried to achieve to the multi-goal optimizing function of economic optimization and energy resource consumption The output setting value of regenerative system, and and reality output deviation as single goal error function, using QPSO algorithms to the list Target error function is solved, and obtains the optimal varied amount of performance variable.
Single goal error function is solved using QPSO algorithms, the process of the optimal varied amount of performance variable is obtained, including Following steps：
S41：It is P to take prediction time domain, and it is M to control time domain, in each moment k, be can obtain：
S42：When P is more than N, yol(k+j | k)=yol(k+N | k), j ＞ N, the predicted value includes the feedback of predicated error Correction and the influence of interference, are obtained：
S43：In dynamic matrix, economic optimization and the multi-goal optimizing function of energy resource consumption are asked according to MQPSO algorithms Solution obtain reaction-regeneration system output setting value, and and reality output deviation be used as single goal error function, selection The single goal error function of minimum is as follows：
In dynamic matrix, the multi-goal optimizing function of economic optimization and energy resource consumption is tried to achieve according to MQPSO algorithms The formula of output setting value that solution obtains reaction-regeneration system is：
In formula (5), yss(k) it is the output setting value of reaction-regeneration system, δ uss(k) for MQPSO algorithms to economic optimization The solution tried to achieve with the multi-goal optimizing function of energy resource consumption,For steady state gain matrix, obtained by the steady-state model of system；For open loop steady state predictions, obtained by the transfer function model recognized.
S44：The object function of minimum is solved using QPSO algorithms, the optimal varied amount of performance variable is obtained.
MATLAB7.0 is used for emulation platform, using RRS as object, is carried out in the research of each algorithm, simulation process, sampling Cycle is 4 minutes, models time domain N=600, performance variable lower limit uiFor -0.5, the performance variable of PREDICTIVE CONTROLThe upper limit is 0.5, controlled variable lower limit yiFor -0.5, the controlled variable upper limitFor 0.5, steady state operation variable change value δ us(k) it is 0.1, behaviour It is 0.1 to make variable change value, in multiple-objection optimization, B1=[0.1 2 2], A1=[10 20 200], J1max=-3, J2max =-4.As shown in Table 1 and Table 2, the parameter value of algorithm is as shown in table 3 for meaning representated by each variable：
Each algorithm parameter value table of table 3
MQPSO-DMPC to the RRS tracking effects exported and to the tracking effect of input as shown in Figure 4 and Figure 5.
It can be seen that by setting RRS economy and energy consumption multi-goal optimizing function, and use from Fig. 4 and Fig. 5 MQPSO is solved to RRS multi-objective optimization question, on the basis of ensureing economic benefit and reducing energy consumption, further to RRS Process carry out stable state control, i.e., the DMPC dynamic matrix control stage is solved using QPSO, simulation result shows, MQPSO-DMPC can be tracked to RRS controlled variable and performance variable, indicate MQPSO-DMPC algorithms having in RRS Effect property.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained Cover within protection scope of the present invention.Therefore, protection scope of the present invention described should be defined by scope of the claims.

Claims (8)

1. a kind of reaction-regeneration system optimal control method based on MQPSO-DMPC, it is characterised in that comprise the following steps：
S1：The transfer function model of reaction-regeneration system is converted into step response model；
S2：DMPC models are set up, DMPC models include open-loop prediction module, steady-state target calculation module and dynamic matrix control mould Block；
S3：It is excellent to economic optimization and the multiple target of energy resource consumption on the premise of not relaxed constraints condition using MQPSO algorithms Change function to be solved；Wherein, the hard constraint and soft-constraint of constraints including performance variable, the hard constraint of controlled variable and soft Constraint, the constraint of external object；
S4：The solution tried to achieve according to MQPSO algorithms to the multi-goal optimizing function of economic optimization and energy resource consumption obtains reaction regeneration The output setting value of system, and and reality output deviation as single goal error function, using QPSO algorithms to the single goal Error function is solved, and obtains the optimal varied amount of performance variable.
2. the reaction-regeneration system optimal control method according to claim 1 based on MQPSO-DMPC, it is characterised in that： The step response model of reaction-regeneration system is：
<mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>A</mi> <mi>i</mi> <mi>u</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>A</mi> <mi>N</mi> <mi>u</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>A</mi> <mi>i</mi> <mi>v</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msubsup> <mi>A</mi> <mi>N</mi> <mi>v</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
In formula (1), Δ u is the variable quantity of performance variable, and k is the time, and N is model length,For the operation of reaction-regeneration system The step-response coefficients matrix of variable,For the step-response coefficients matrix of the disturbance variable of reaction-regeneration system, forMeet
3. the reaction-regeneration system optimal control method according to claim 1 based on MQPSO-DMPC, it is characterised in that： The process of open-loop prediction module is set up, is comprised the following steps：
S211：As Δ u (k+i-1)=0, Δ v (k+i-1)=0 (1≤i≤P), ifFor to the pre- of y (k+p | k) Measured value, wherein, Δ ν is the variable quantity of disturbance variable, and P is prediction time domain, then has：
<mrow> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>p</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>y</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>p</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>A</mi> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> <mi>u</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>A</mi> <mi>p</mi> <mi>v</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>v</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
S212：Consider feedback compensation, it is assumed that vss(k)=vss(k-1)+Δ v (k) is the reaction regeneration system, it is known that since the k moment When the performance variable of system no longer changes, the open-loop prediction for obtaining reaction-regeneration system based on formula (2) is yol(k+i | k), work as detection The open-loop prediction of reaction-regeneration system is obtained to solution when Δ u (k-1)：
<mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>A</mi> <mn>1</mn> <mi>u</mi> </msubsup> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein, vss(k) it is the recurrence model of step response.
4. the reaction-regeneration system optimal control method according to claim 1 based on MQPSO-DMPC, it is characterised in that： The process of steady-state target calculation module is set up, is comprised the following steps：
S221：The performance variable of all reaction-regeneration systems and the hard constraint condition of controlled variable and soft-constraint condition are extracted, and Merge the variable quantity δ u being expressed as on steady state operation variabless(k) form：
Wherein,For the upper limit of performance variable,For the set of the ideal value of performance variable,For steady state gain matrix,For the variable quantity of stable state controlled variable,For the set of the ideal value of controlled variable, k is iterations, when t is Between；
S222：Set up economic optimization J1J is consumed with energy consumption2Biobjective scheduling function：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>min</mi> <mi> </mi> <msub> <mi>J</mi> <mn>1</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;NotElement;</mo> <msub> <mi>&amp;Psi;</mi> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </msub> </mrow> </munder> <msub> <mi>B&amp;delta;u</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mrow> <mn>1</mn> <mi>min</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <msub> <mi>&amp;Psi;</mi> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </msub> </mrow> </munder> <msup> <mi>B</mi> <mn>2</mn> </msup> <msub> <mi>U</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>min</mi> <mi> </mi> <msub> <mi>J</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;NotElement;</mo> <msub> <mi>&amp;Psi;</mi> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </msub> </mrow> </munder> <msub> <mi>B&amp;delta;u</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mo>(</mo> <mi>k</mi> <mo>)</mo> <mo>-</mo> <msub> <mi>J</mi> <mrow> <mn>2</mn> <mi>min</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>&amp;Element;</mo> <msub> <mi>&amp;Psi;</mi> <mrow> <mi>m</mi> <mi>m</mi> </mrow> </msub> </mrow> </munder> <msup> <mi>B</mi> <mn>2</mn> </msup> <msub> <mi>U</mi> <mi>i</mi> </msub> <msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
In formula (3), B is weight,
S223：Relaxed constraints condition, is solved using QUADRATIC PROGRAMMING METHOD FOR to formula (3), obtains the steady state operation under multiple target The variable quantity δ u of variabless(k)。
5. the reaction-regeneration system optimal control method according to claim 1 based on MQPSO-DMPC, it is characterised in that： The process of dynamic matrix control module is set up, is comprised the following steps：
S231：It is P to take prediction time domain, and it is M to control time domain, in each moment k, be can obtain：
<mrow> <msubsup> <mi>Y</mi> <mi>P</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
S232：When P is more than N, yol(k+j | k)=yol(k+N | k), j ＞ N, the predicted value includes the feedback compensation of predicated error And the influence of interference, obtain：
<mrow> <msub> <mi>Y</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>Y</mi> <mi>P</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>D</mi> <mi>&amp;Delta;</mi> <mover> <mi>u</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow>
Wherein, D is dynamic control matrix；
S233：In dynamic matrix, the multi-goal optimizing function of economic optimization and energy resource consumption is tried to achieve according to MQPSO algorithms Solution obtains the output setting value of reaction-regeneration system, and regard the deviation of the output setting value and reality output as single goal error Function, selects the single goal error function minimized as follows：
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mn>1</mn> <mi>P</mi> </munderover> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>|</mo> <mi>k</mi> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>j</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mo>^</mo> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Wherein, Q (k) is weighting matrix；
S234：The object function of minimum is solved, the optimal varied amount of steady state operation variable is obtained.
6. the reaction-regeneration system optimal control method according to claim 4 based on MQPSO-DMPC, it is characterised in that： Using MQPSO algorithms, on the premise of not relaxed constraints condition, economic optimization and the multi-goal optimizing function of energy resource consumption are entered The process that row is solved, comprises the following steps：
S31：Systematic parameter, including population scale n, maximum iteration T are initialized, at random n particle x of generation1,x2..., xn、 Particle dimension m, compression-broadening factor α and external archival collection Q is made, Q is sky；
S32：The fitness of each particle is evaluated, and individual optimal value and global optimum are replaced according to quality；
S33：By the current fitness p of each particleiWith individual adaptive optimal control degreeIt is compared, if current fitness piBranch With individual adaptive optimal control degreeThen by current fitness piInstead of individual adaptive optimal control degreeOtherwise, original individual is retained most Excellent fitness
S34：External archival collection Q is updated, non-dominant collection all in population external archival collection Q is added into, and delete what is dominated Particle；
S35：A particle is randomly choosed in external archival collection Q be used as global optimum by the use of press mechanism and Tabu search algorithm；
S36：Update the position x of the particle as global optimumij(t), more new formula is：
xij(t+1)=eij(t)±α|Cij(t)-xij(t)|×ln[1/uij(t)]
<mrow> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mn>1</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mn>2</mn> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <mn>...</mn> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>P</mi> <mrow> <mi>i</mi> <mi>m</mi> </mrow> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
eij(t)=β Pij(t)+(1-β)Pgj(t)
<mrow> <mi>&amp;alpha;</mi> <mo>=</mo> <mn>1</mn> <mo>-</mo> <mn>0.5</mn> <mo>&amp;times;</mo> <mfrac> <mi>t</mi> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mfrac> <mo>;</mo> </mrow>
Wherein, Cij(t) the average optimal position of all particles, x are representedij(t+1) particle for being denoted as global optimum updates Position afterwards, PijFor the current optimal location of i-th of particle jth dimension, PgjFor global optimum position, uijWith β be respectively 0 to 1 it Between random number；
S37：Judge whether current globally optimal solution meets condition or whether iterations reaches maximum iteration T, if It is then to export current globally optimal solution, otherwise, jumps to step S32 and computed repeatedly, until current globally optimal solution is met Untill condition or iterations reach maximum iteration T；
S38：Relaxed constraints condition, does not utilize economic optimization Js of the MQPSO to foundation1J is consumed with energy consumption2Biobjective scheduling function Solved, obtain the variable quantity δ u of the steady state operation variable under multiple targetss(k)。
7. the reaction-regeneration system optimal control method according to claim 1 based on MQPSO-DMPC, it is characterised in that： Single goal error function is solved using QPSO algorithms, the process of the optimal varied amount of performance variable is obtained, comprises the following steps：
S41：It is P to take prediction time domain, and it is M to control time domain, in each moment k, be can obtain：
<mrow> <msubsup> <mi>Y</mi> <mi>P</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mn>2</mn> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>y</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msup> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>P</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
S42：When P is more than N, yol(k+j | k)=yol(k+N | k), j ＞ N, feedback compensation of the predicted value comprising predicated error and The influence of interference, is obtained：
<mrow> <msub> <mi>Y</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>Y</mi> <mi>P</mi> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>D</mi> <mi>&amp;Delta;</mi> <mover> <mi>u</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <mi>k</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow>
S43：In dynamic matrix, the multi-goal optimizing function of economic optimization and energy resource consumption is tried to achieve according to MQPSO algorithms Solution obtains the output setting value of reaction-regeneration system, and and reality output deviation as, single goal error function, selection is minimum The single goal error function J (k) of change is as follows：
<mrow> <mi>J</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mn>1</mn> <mi>P</mi> </munderover> <mo>|</mo> <mo>|</mo> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>|</mo> <mi>k</mi> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mrow> <mi>Q</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mo>|</mo> <mo>|</mo> <mi>&amp;Delta;</mi> <mi>u</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>+</mo> <mi>j</mi> <mo>|</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mo>^</mo> <mn>2</mn> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
S44：The object function of minimum is solved using QPSO algorithms, the optimal varied amount of performance variable is obtained.
8. the reaction-regeneration system optimal control method according to claim 7 based on MQPSO-DMPC, it is characterised in that： In dynamic matrix, the solution tried to achieve according to MQPSO algorithms to the multi-goal optimizing function of economic optimization and energy resource consumption obtains anti- The formula for answering the output setting value of regenerative system is：
<mrow> <msub> <mi>y</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>S</mi> <mi>N</mi> <mi>u</mi> </msubsup> <msub> <mi>&amp;delta;u</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>y</mi> <mrow> <mi>s</mi> <mi>s</mi> </mrow> <mrow> <mi>o</mi> <mi>l</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In formula (5), yss(k) it is the output setting value of reaction-regeneration system, δ uss(k) for MQPSO algorithms to economic optimization and the energy The solution that the multi-goal optimizing function of consumption is tried to achieve,For steady state gain matrix；For open loop steady state predictions.
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